For a given point and a circle, the product of the lengths of the two segments from the point to the circle is constant along any line through the point and circle.
sqrt(10)
Practice makes perfect
Let's consider the given diagram.
We can see that one of its chords is going through the center of the circle. Therefore, this chord is a diameter. Moreover, since both chords are perpendicular, the diameter divides the other chord into segments of same lengths.
Recall that the product of the lengths of the two segments from the point to the circle is constant along any line through the point and circle. In our diagram, the point which will follow this rule is the point of intersection of the shown chord segments. Therefore, the products of the lengths of the chord segments are equal.
x * x= 2 * 5
Let's solve this equation for x.
